Absolute vs. Relative Gromov-Witten Invariants

Mohammad F. Tehrani, Aleksey Zinger

Published 2014-05-08, updated 2014-05-12Version 2

In light of recent attempts to extend the Cieliebak-Mohnke approach for constructing Gromov-Witten invariants to positive genera, we compare the absolute and relative Gromov-Witten invariants of compact symplectic manifolds when the symplectic hypersurface contains no relevant holomorphic curves. We show that these invariants are then the same, except in a narrow range of dimensions of the target and genera of the domains, and provide examples when they fail to be the same.